1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to a method for inversion of measurements made by multi-component induction or propagation sensors.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound such that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
Baker Atlas and Shell International EandP jointly developed a new multicomponent induction logging tool, 3DEX to measure the electrical anisotropy of these sequences. This logging tool and its use is described in U.S. Pat. No. 6,147,496 to Strack et al. The instrument comprises three mutually orthogonal transmitter-receiver configurations that provide all necessary data to compute horizontal and vertical resistivities of the formation. These resistivities may then be used in an integrated petrophysical analysis to provide an improved estimate of the laminar sand resistivity and corresponding net oil-in-place.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the xe2x80x9cGupta patentxe2x80x9d), the contents of which are fully incorporated here by reference, discloses a method for determination of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to a one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate Measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes, which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
However, the new horizontal magnetic field responses, Hxx and Hxx, that are sensitive to the vertical resistivity of the formation can suffer from strong borehole and near-zone effects. These effects increase with borehole size, borehole fluid conductivity, and invasion depth. Co-pending U.S. patent application Ser. No. 09/676,097 U.S. Pat No. 6,466,872, by Kriegshxc3xa4user et al. describes a method for applying shoulder bed corrections to this data. However, in large borehole sizes and conductive mud systems, these corrections cannot completely eliminate the near-zone effects.
However, a rigorous 2-D inversion is too time-intensive and prohibitive for typical logging applications, because the 2-D forward model response is time consuming and also because inversion schemes typically require the determination of a Jacobian matrix defining the sensitivity of each of the measurements to every one of the parameters in the model.
Tabarovsky and Rabinovich (U.S. Pat. No. 5,703,773) teach a computationally fast method for 2-D inversion of induction logging data. The method includes skin effect correcting the responses of the receivers by extrapolating the receiver responses to zero frequency. A model is generated of the media surrounding said instrument. Conductivities of elements in the model are then adjusted so that a measure of misfit between the skin-effect corrected receiver responses and simulated receiver responses based on the model is minimized. The geometry of the model is then adjusted so that the measure of misfit between the skin-effect corrected receiver responses and the simulated receiver responses based on the model is further minimized. In a preferred embodiment of the invention, the step of adjusting the geometry includes minimizing the measure of misfit between the simulated responses and the receiver responses from selected ones of the receivers closely spaced to the transmitter. Numbers of and positions of radial boundaries are then determined by minimizing the measure of misfit for all the receiver responses. However, Tabarovsky does not address the problem of inversion of multi-component data.
There is a need for a method of inversion of multicomponent induction logging data that gives reasonably accurate results without using an inordinate amount of computer time. The present invention satisfies this need.
An electromagnetic logging tool having a plurality of transmitters and receivers (3DEX) is used to obtain multicomponent measurements indicative of horizontal and vertical resistivities of subsurface formations. A model for the horizontal resistivity, length of the invasion zone and resistivity of the invasion zone may be obtained from High Definition Induction Logging (HDIL) tools. Such an induction logging tool comprises transmitter and receiver coils with axes parallel to the tool axis: measurements are made at multiple frequencies and/or with multiple transmitter-receiver spacings. An example of such a tool is given in U.S. Pat. No. 5,452,761 to Beard et al. An initial model is defined that includes the obtained model and vertical resistivities for the formations. In one embodiment of the invention, the vertical resistivities for the initial model are set equal to the horizontal resistivities. In alternate embodiment of the invention, the horizontal and vertical resistivities may be related by a predefined anisotropy factor. A 2-D forward response modeling is carried out and a difference between the model output and the actual measurements made with the 3DEX is determined. If the difference is small, the model is acceptable. Otherwise, the model is iteratively updated with only a subset of the model parameters being changed, so as to reduce the difference. The updating uses only the sensitivity of a subset of the measurements to the subset of the model parameters being changed.
In a preferred embodiment of the invention, the subset of the model parameters being changed includes the layer horizontal and vertical resistivities, while the layer thicknesses, length of the invasion zone and resistivity of the invasion zone are kept fixed.
In a preferred embodiment of the invention, the subset of measurements for which the sensitivity is used includes the Hzz component and at least one of (i) the Hxx component, (ii) the Hyy component, and, (iii) an average of the Hxx and Hyy components.